Method for Generating Digital Quantum Chaotic Wavepacket Signals

ABSTRACT

A method for generating digital quantum chaotic orthonormal wavepacket signals includes the following steps: construct a N-dimensional Hermitian matrix Ĥ; calculate N eigen-wavefunctions φj of a quantum Hamiltonian system with the Hamiltonian Ĥ by some numerical calculation methods, wherein the Hamiltonian is the Hermitian matrix Ĥ; extract some or all of the eigen-functions φj with obvious chaos features as quantum chaotic eigen-wavefunctions according to a chaos criterion; generate some semi-classical digital quantum chaotic wavepacket signals φj(n) with the same mathematical form as the quantum chaotic eigen-wavefunctions and length N from the selected quantum chaotic eigen-wavefunctions according to the mathematical correspondence between the classical signal and the wavefunction in quantum mechanics. By combining the quantum state chaotic transition theory and the classical time-frequency analysis, some semi-classical quantum chaotic wavepacket digital signals are generated according to the mathematical correspondence between the classical time-frequency signal and the wavefunction in quantum mechanics.

CROSS REFERENCE TO THE RELATED APPLICATIONS

This application is the national phase entry of InternationalApplication No. PCT/CN2018/079278, filed on Mar. 16, 2018, the entirecontents of which are incorporated herein by reference.

TECHNICAL FIELD

The invention relates to radio communication and radar, especially amethod for generating digital quantum chaotic wavepacket signals.

BACKGROUND

With some excellent characteristics, such as sensitivity to initialstates, pseudo randomness, aperiodicity, noise-like wideband and sharpautocorrelation, the classical chaotic signals have vast applicationprospect in radio communication and radar theoretically. However, theyare not practical due to the impossible completion of chaotic carriersynchronization under interference.

Kehui Sun elaborated the classical chaotic signal and its application,analysis methods and typical systems in his masterworks “the principleand technology of chaotic secure communication” published by theTsinghua University Press in February 2015, and focused on the basictechniques and methods involved in chaotic secure communication system,including chaotic carrier synchronous control technology, chaotic securecommunication system scheme, chaotic encryption system principle anddesign, chaotic circuit design and implementation technology. Accordingto the chaotic synchronization method described in this book, thecommunication performance such as the information transmission rate andthe bit error rate would deteriorate sharply due to the interference.

SUMMARY

In order to solve the above technical problems, a method for generatingdigital quantum chaotic wavepacket signals is proposed in the presentinvention. By combining the quantum state chaotic transition theory andthe classical time-frequency analysis, some semi-classical and digitalquantum chaotic wavepacket signals are generated according to themathematical correspondence between the classical time-frequency signaland the wavefunction in quantum mechanics. These signals not only havethe almost identical features to the classical chaotic ones, so as tosolve the problems of chaotic synchronization, but also have uniquesplitting spectrum so as to eliminate the spectrum leakage problem ofBOC signal widely used in GNSS. Significantly, the novel digital quantumchaotic wavepacket signals have excellent compatibility with theclassical sinusoidal ones.

The method for generating digital quantum chaotic wavepacket signals inthe invention comprises the following steps:

Step one: construct a N×N Hermitian matrix Ĥ;

Step two: calculate the N eigen-wavefunctions φ_(j) of the quantumHamiltonian system with the Hamiltonian by some numerical calculationmethods, wherein the Hamiltonian is the N×N Hermitian matrix Ĥ;

Step three: extract some or all of the eigen-wavefunctions φ_(j) withobvious chaos features as quantum chaotic wavefunctions according to achaos criterion;

Step four: generate some semi-classical and digital quantum chaoticwavepacket signals φ_(j)(n) with the same mathematical form as that ofthe quantum chaotic eigen-wavefunctions and length N from the selectedquantum chaotic wavefunctions according to the mathematicalcorrespondence between the classical signal and the wavefunction inquantum mechanics.

Preferably, the N×N Hermitian matrix Ĥ used as a Hamiltonian of aquantum Hamiltonian system, has the following mathematical expression:

${\overset{\hat{}}{H}\left( {x,y} \right)} = {{- \frac{a}{\sigma}}e^{\frac{{({x - y})}^{2}}{b\sigma^{2}}}}$

wherein the a, b and σ are specific constant parameters.

In any of the above technical solutions, it is preferred that thequantum Hamiltonian system with the Hamiltonian has quantum statechaotic transition, which is characterized that some of itseigen-wavefunctions have the similar unique features to the classicalchaotic signals, wherein the Hamiltonian is the N×N Hermitian matrix Ĥ.

In any of the above technical solutions, it is preferred that theeigen-wavefunction φ_(j) must meet the following mathematicalconstraint:

Ĥφ _(j) =E ₂φ_(j);

wherein the E_(j) is the energy level of a quantum corresponding to theeigen-wavefunction φ_(j).

In any of the above technical solutions, it is preferred that thementioned numerical calculation methods include the Divide and ConquerMethod or the Jacobian Method or both of them.

In any of the above technical solutions, it is preferred that anunavoidable Hermitian external perturbation H′ is added to the originalHermitian Hamiltonian Ĥ to get some very different eigen-vectors φ_(j)by any numerical calculation method.

(Ĥ+H′)φ_(j) =E _(j)φ_(j)

In any of the above technical solutions, it is preferred that themomentum spectral density is used as the mentioned chaos criterion bythe self-power spectrum density method.

In any of the above technical solutions, it is preferred that accordingto the chaos criterion, the momentum spectral density ψ₁ is calculatedby the Fourier Transform of the eigen-wavefunctions φ_(j) firstly.

In any of the above technical solutions, it is preferred that accordingto the chaos criterion, the chaotic property of the eigen-wavefunctionφ_(j) is determined by its corresponding momentum spectral density ψ₁.

In any of the above technical solutions, it is preferred that aneigen-wavefunction φ_(j) with obviously extended momentum spectraldensity is chaotic, and is quantum chaotic wavefunction.

A method for generating digital quantum chaotic wavepacket signals isproposed in the invention. The digital quantum chaotic wavepacketsignals which is obtained by calculating the chaotic eigen-wavefunctionsof a specified quantum Hamiltonian system not only have the samefeatures as classical chaotic ones, but also have the unique splittingspectrum characteristic that makes it similar to non-white noise. Theabove semi-classical and digital quantum chaotic wavepacket signals cannot only solve chaotic carrier synchronization in classical chaoticsecure communication, but also provide excellent compatibility with theclassical sinusoidal ones.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow chart of the method for generating digital quantumchaotic wavepacket signals according to a preferred embodiment of theinvention.

FIG. 2 is a block diagram of the direct quantum chaotic wavepacketunified radio system according to a preferred embodiment of theinvention.

FIG. 2A is a block diagram of the frequency-converted quantum chaoticwavepacket unified radio system according to the preferred embodiment ofthe invention shown in FIG. 2.

FIG. 2B is a work flow chart of the quantum chaotic wavepacket unifiedradio system according to the preferred embodiment of the inventionshown in FIG. 2.

FIG. 2C is a flow chart for generating and allocating the quantumchaotic wavepacket signal according to the preferred embodiment of theinvention shown in FIG. 2.

FIG. 3 is a flow chart of the quantum chaotic wavepacket shift keyingcommunication according to the preferred embodiment of the inventionshown in FIG. 2.

FIG. 3A is a flow chart of the orthonormal wavepacket transformconfidential lossy compression according to the preferred embodiment ofthe invention shown in FIG. 3.

FIG. 4 is a block diagram of the quantum chaotic wavepacket synchronousdemodulation module according to the preferred embodiment of theinvention shown in FIG. 2.

FIG. 4A is a work flow chart of the quantum chaotic wavepacketsynchronous demodulation module according to the preferred embodiment ofthe invention shown in FIG. 4.

FIG. 5 is a work flow chart of the orthonormal wavepacket inversetransform decompression module for original image or data according tothe preferred embodiment of the invention shown in FIG. 2.

FIG. 6 is a block diagram of the quantum chaotic wavepacket primaryradar according to the preferred embodiment of the invention shown inFIG. 2.

FIG. 6A is a block diagram of the quantum chaotic wavepacket primaryradar target recognition according to the preferred embodiment of theinvention shown in FIG. 6.

FIG. 6B is a work flow chart of the quantum chaotic wavepacket primaryradar target recognition according to the preferred embodiment of theinvention shown in FIG. 6.

FIG. 7 is a block diagram of the quantum chaotic wavepacket secondaryradar according to the preferred embodiment of the invention shown inFIG. 2.

FIG. 7A is a block diagram of the quantum chaotic wavepacket secondaryradar signal generation according to the preferred embodiment of theinvention shown in FIG. 7.

FIG. 7B is a work flow chart of quantum chaotic wavepacket secondaryradar signal generation according to the preferred embodiment of theinvention shown in FIG. 7.

FIG. 7C is a block diagram of the quantum chaotic wavepacket secondaryradar target recognition according to the preferred embodiment of theinvention shown in FIG. 7.

FIG. 7D is a work flow chart of the preferred scheme for the quantumchaotic wavepacket secondary radar target recognition according to thepreferred embodiment of the invention shown in FIG. 7.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The present invention is further elaborated in accordance with thedrawings and embodiments.

Embodiment 1

By combining the quantum state chaotic transition theory and theclassical time-frequency analysis, some semi-classical and digitalquantum chaotic wavepacket signals are generated according to themathematical correspondence between the classical time-frequency signaland the wavefunction in quantum mechanics, These digital signals notonly have the same features as the classical chaotic ones, but also havethe unique splitting spectrum characteristic. The semi-classical anddigital quantum chaotic wavepacket signals are generated through thefollowing procedures shown in FIG. 1.

Executing step 100: construct a N×N Hermitian matrix Ĥ as theHamiltonian of a quantum Hamiltonian system, and the Hermitian matrix Ĥhas the following mathematical expression:

${\overset{\hat{}}{H}\left( {x,y} \right)} = {{- \frac{a}{\sigma}}e^{\frac{{({x - y})}^{2}}{b\; \sigma^{2}}}}$

wherein the a, b and σ are specific constant parameters.

Executing step 110: calculate the N eigen-wavefunctions φ_(j) of thequantum Hamiltonian system with the Hamiltonian by some numericalcalculation methods, wherein the Hamiltonian is the N×N Hermitian matrixĤ, and the eigen-wavefunction φ_(j) meets the following mathematicalconstraint:

Ĥφ _(j) =E _(j)φ_(j)

wherein the E_(j) is the energy level of a quantum corresponding to theeigen-wavefunction φ_(j). Furthermore, an unavoidable Hermitian externalperturbation H′ is added to the original Hermitian Hamiltonian Ĥ to getsome very different eigen-vectors φ_(j) by any numerical calculationmethod including the Divide and Conquer Method, the Jacobian Method andso on.

(Ĥ+H′)φ_(j) =E _(j)φ_(j)

Executing step 120: momentum spectral density is used as a chaoscriterion to extract some or all of the eigen-wavefunctions φ_(j) withobvious chaos features as quantum chaotic wavefunctions. As for thechaos criterion, the chaotic property of the eigen-wavefunction φ_(j) isdetermined by its corresponding momentum spectral density ψ_(j) whichequals to its Fourier Transform. Specifically, an eigen-wavefunctionφ_(j) with obviously extended momentum spectral density is chaotic.

Executing step 130, generate some semi-classical and digital quantumchaotic wavepacket signals φ_(j)(n) with the same mathematical form asthat of the quantum chaotic eigen-wavefunctions and length N from theselected quantum chaotic eigen-wavefunctions according to themathematical correspondence between the classical signal and thewavefunction in quantum mechanics.

Embodiment 2

The quantum chaotic wavepacket unified radio system is a unifiedsoftware defined radio (SDR) system which unifies the quantum chaoticwavepacket secure communication, the quantum chaotic wavepacket primaryradar and the quantum chaotic wavepacket secondary radar. Theall-digital, multifunctional and configurable quantum chaotic wavepacketunified radio system is classified into two categories: the directquantum chaotic wavepacket unified radio system shown in FIG. 2 and thefrequency-converted quantum chaotic wavepacket unified radio systemshown in FIG. 2A.

The quantum chaotic wavepacket unified radio system consists of aquantum chaotic wavepacket shift keying secure communication sub-system,a quantum chaotic wavepacket primary radar sub-system and a quantumchaotic wavepacket secondary radar sub-system. As shown in FIG. 2B, thewhole workflow of the quantum chaotic wavepacket unified radio systemconsists of four sub-processes, wherein digital quantum chaoticwavepacket signal generation and allocation subprocess 200 must becarried out first, then at least one of quantum chaotic wavepacket shiftkeying secure communication subprocess 210, quantum chaotic wavepacketprimary radar target detection subprocess 220 and quantum chaoticwavepacket secondary radar target recognition subprocess 230 should becarried out.

I. Subprocess 200: Generate and Allocate the Digital Quantum ChaoticWavepacket Signals According to the Specific System Requirement.

The fundamental digital quantum chaotic orthonormal wavepacket signalgeneration and allocation subprocess 200 is accomplished through thefollowing procedures sequentially as shown in FIG. 2C.

Executing procedure 250: construct a N×N Hermitian matrix Ĥ.

${\overset{\hat{}}{H}\left( {x,y} \right)} = {{- \frac{a}{\sigma}}e^{\frac{{({x - y})}^{2}}{b\sigma^{2}}}}$

wherein the a, b and σ are specific constant parameters.

Executing procedure 251: calculate the eigenvectors φ_(j) of theHermitian matrix Ĥ by some numerical calculation methods such as theDivide and Conquer Method, the Jacobian Method, etc.

Ĥφ _(j) =E _(j)φ_(j)

Executing procedure 252: extract some or all of the eigenvectors φ_(j)with obvious chaos features according to a chaos criterion by theself-power spectrum density method.

Executing procedure 253: generate J semi-classical and digital quantumchaotic wavepacket signals φ_(j)(n) with length N according to themathematical correspondence between the classical signal and thewavefunction in quantum mechanics.

Executing procedure 254: allocate these above digital quantum chaoticwavepacket signals to the quantum chaotic wavepacket shift keying securecommunication φ_(j1)(n) and φ_(j2)(n), the quantum chaotic wavepacketprimary radar target detection φ_(j3)(n) and the quantum chaoticwavepacket secondary radar target recognition φ_(j4)(n) according tosome optimization principles, such as EMC, etc.

II. Optional Subprocess 210: Implement Quantum Chaotic Wavepacket ShiftKeying Secure Communication

The optional quantum chaotic wavepacket shift keying securecommunication subprocess 210 includes five sequential procedure, theoptional original image or data orthonormal wavepacket transform lossycompressing procedure 301, the quantum chaotic wavepacket shift keyingmodulation procedure 302, the quantum chaotic wavepacket signaltransmit-receiving procedure 303, the quantum chaotic wavepacketsynchronous demodulation procedure 304 and the optional orthonormalwavepacket inverse transform decompressing procedure 305 as shown inFIG. 3.

1. [Optional] the Original Image or Data Orthonormal WavepacketTransform Lossy Compressing Procedure 301

The optional original image or data orthonormal wavepacket transformlossy compressing procedure 301 accomplishes the data lossy compressionto improve communication efficiency by twice orthogonal wavepackettransforms following the three steps sequentially shown in FIG. 3A.

Executing procedure 310: perform the orthonormal wavepacket transform onthe original image or data P_(t) _(N×N) by rows to get an intermediatedata P_(t) ¹ _(N×N)

${P_{t}^{1}\left( {i,j} \right)} = {\sum\limits_{k}{{P_{t}\left( {i,k} \right)}{\phi_{j}(k)}}}$

Executing procedure 320: perform the orthonormal wavepacket transform onthe above intermediate data P_(t) ¹ _(N×N) by columns to get the finaltransformed data P_(t) ² _(N×N).

${P_{t}^{2}\left( {i,j} \right)} = {\sum\limits_{k}{{P_{t}^{1}\left( {k,j} \right)}{\phi_{i}(k)}}}$

Executing procedure 330: perform the lossy compression of the abovefinal transformed data P_(t) ² _(N×N) by discarding some minor data suchas the data below the threshold

² so as to get a small amount of compressed data [m, n, P²].

[m,n,P ²]={|P _(t) ²(m,n)|>

²}

2. The Quantum Chaotic Wavepacket Shift Keying Modulation Procedure 302

The fundamental quantum chaotic wavepacket shift keying modulationprocedure 302 implements the quantum chaotic wavepacket carriers φ_(j1)and φ_(j2) shift keying modulation with the input binary data D(n) toget quantum chaotic wavepacket baseband signal s_(t) ^(Comm)(n) forsecure communication.

${s_{t}^{Comm}(n)} = \left\{ \begin{matrix}{\phi_{j\; 1}\left( {n\% N} \right)} & {{D\left( \left\lbrack \frac{n}{N} \right\rbrack \right)} = 0} \\{\phi_{j\; 2}\left( {n\% N} \right)} & {{D\left( \left\lbrack \frac{n}{N} \right\rbrack \right)} = 1}\end{matrix} \right.$

wherein the N is the length of the quantum chaotic wavepacket carrier.

3. The Quantum Chaotic Wavepacket Signal Transmit-Receiving Procedure303

The fundamental quantum chaotic wavepacket signal transmit-receivingprocedure 303 mainly accomplishes the transmission and reception of thequantum chaotic wavepacket baseband signal. In the transmitter, thequantum chaotic wavepacket baseband signal is transmitted eitherdirectly or frequency converted, correspondingly in the receiver thequantum chaotic wavepacket baseband signal is received either directlyor frequency converted, as shown in FIG. 2 and FIG. 2A.

4. The Quantum Chaotic Wavepacket Synchronous Demodulation Procedure 304

The quantum chaotic wavepacket synchronous demodulation procedure 304mainly accomplishes the quantum chaotic wavepacket carriersynchronization with the received baseband signal and demodulation toextract the modulated data D(n). The block diagram which executes theprocedure 304 is shown in FIG. 4, and the procedure 304 following thethree steps sequentially is shown in FIG. 4A.

Executing procedure 400: accomplish the temporal digital correlationbetween the received baseband signal s_(r) and the quantum chaoticwavepacket carriers φ_(j1) and φ_(j2) to get two nonnegative correlationvalue sequences by the sliding inner-product separately,

${R_{j}(k)} = {{\sum\limits_{n}{{s_{r}\left( {n + k} \right)}{\phi_{j}(n)}}}}^{2}$

wherein the j is j1 or j2.

Executing procedure 410: accomplish the quantum chaotic carriersynchronization by the summation I^(sync) of the K span of the above twononnegative correlation value sequences R_(j1)(k) and R_(j2)(k),

${I^{sync}(n)} = {\sum\limits_{k}{\sum\limits_{j}{R_{j}\left( {n - k} \right)}}}$

wherein j=j1,j2; k=1,2, . . . , K. Meanwhile, the separate summationI_(j) ^(Demod) of the M span of the above two nonnegative correlationvalue sequences R_(j1)(k) and R_(j2)(k) is calculated, and normally M is5 to 8 larger than K.

${I_{j}^{Demod}(n)} = {\sum\limits_{m}{R_{j}\left( {n - m} \right)}}$

wherein j=j1, j2; m=1, 2, . . . , M.

Executing procedure 420: extract the modulated data D by comparison theabove separate summation I_(j1) ^(Demod) and I_(j2) ^(Demod) at thecorrelating synchronization time k₀ when the I^(sync) is equal orgreater than a synchronous threshold I_(ref).

${\hat{D}\left( k_{0} \right)} = \left\{ \begin{matrix}0 & {{I_{j\; 1}^{Demod}\left( k_{0} \right)} \geq {I_{j\; 2}^{Demod}\left( k_{0} \right)}} \\1 & {{I_{j\; 1}^{Demod}\left( k_{0} \right)} < {I_{j\; 2}^{Demod}\left( {nk}_{0} \right)}}\end{matrix} \right.$

5. [Optional] the Original Image or Data Orthonormal Wavepacket InverseTransform Decompressing Procedure 305

The optional orthonormal wavepacket inverse transform decompressingprocedure 305 accomplishes the image or data decompression by twiceorthonormal wavepacket inverse transforms following the three stepssequentially shown in FIG. 5.

Executing procedure 500: preprocess the received image or data byreconstructing [m, n, P²] of {circumflex over (D)}(n) to a correspondingN-order square matrix P_(r) ².

Executing procedure 510: perform the orthonormal wavepacket inversetransform on the above reconstructed matrix P_(r) ² by columns to getthe intermediate inverse transformed data P_(r) ¹ _(N×N).

${P_{r}^{1}\left( {i,j} \right)} = {\sum\limits_{k}{{P_{r}^{2}\left( {k,j} \right)}{\phi_{i}(k)}}}$

Executing procedure 520: perform the orthonormal wavepacket inversetransform on the above intermediate inverse matrix P_(r) ¹ _(N×N) byrows to get the final decompressed data P_(t) ¹ _(N×N).

${P_{r}\left( {i,j} \right)} = {\sum\limits_{k}{{P_{r}^{1}\left( {i,k} \right)}{\phi^{j}(k)}}}$

III. Optional Subprocess 220: Implement Quantum Chaotic WavepacketPrimary Radar Target Detection

The quantum chaotic wavepacket primary radar target detection subprocess220 is optional and includes three sequential procedures, the quantumchaotic wavepacket primary radar signal generating procedure 600, thequantum chaotic wavepacket signal transmit-receiving procedure 601 andthe quantum chaotic wavepacket primary radar target detection procedure602 as shown in FIG. 6.

1. The Quantum Chaotic Wavepacket Primary Radar Signal GeneratingProcedure 600

The fundamental quantum chaotic wavepacket primary radar signalgenerating procedure 600 mainly generates the quantum chaotic wavepacketprimary radar baseband signal s_(t) ^(PriRadar) by transmitting therecurrent quantum chaotic wavepacket carrier φ_(j3).

s _(t) ^(PriRadar)(n)=φ_(j3)(n% N)

wherein the N is the length of the quantum chaotic wavepacket primaryradar carrier.

2. The Quantum Chaotic Wavepacket Signal Transmit-Receiving Procedure601

The fundamental quantum chaotic wavepacket signal transmit-receivingprocedure 601 mainly accomplishes the transmission and reception of thequantum chaotic wavepacket primary radar baseband signal. In thetransmitter, the quantum chaotic wavepacket primary radar basebandsignal is transmitted either directly or frequency converted,correspondingly in the receiver the quantum chaotic wavepacket primaryradar baseband signal is received either directly or frequencyconverted, as shown in FIG. 2 and FIG. 2A.

3. The Quantum Chaotic Wavepacket Primary Radar Target DetectionProcedure 602

The fundamental quantum chaotic wavepacket primary radar targetdetection module 602 mainly detects the interested target and extractsits information such as two-way delay by the correlation detection ofthe quantum chaotic wavepacket primary radar carrier in the receivedradar baseband signal shown in FIG. 6A following the three stepssequentially shown in FIG. 6B.

Executing procedure 610: perform the temporal digital correlationbetween the received radar baseband signal s_(r) and the transmittedquantum chaotic wavepacket primary radar carrier φ_(j3) to get anonnegative correlation value sequence R_(j3) by the slidinginner-product.

${R_{j\; 3}(k)} = {{\sum\limits_{n}{{s_{r}\left( {n + k} \right)}{\phi_{j\; 3}(n)}}}}^{2}$

Executing procedure 620: find the maximum R_(max) and its correspondingtime delay k₀ in the span 2K of the above nonnegative correlation valuesequence R_(j3) (k).

R _(j3)(k ₀)=R _(max)

Executing procedure 630: generate the primary radar target detectionreturn-to-zero pulse by compare the maximum primary radar nonnegativecorrelation value R_(j3) (k₀) with the threshold R_(ref).

Executing procedure 640: estimate the two-way delay of the quantumchaotic wavepacket primary radar target by a normalized and weightedsummation of the above nonnegative correlation value sequence R_(j3)(k)by the trigger of the above primary radar target detectionreturn-to-zero pulse.

$k = {k_{0} + {\sum\limits_{k = {- K}}^{K}{k\frac{R_{j\; 3}\left( {k_{0} + k} \right)}{R_{\max}}}}}$

Iv. Optional Subprocess 230 Implement Quantum Chaotic WavepacketSecondary Radar Target Recognition

The optional quantum chaotic wavepacket secondary radar targetrecognition subprocess 230 is optional and includes three procedures,the quantum chaotic wavepacket secondary radar signal generatingprocedure 700, the quantum chaotic wavepacket secondary radar signaltransmit-receiving procedure 701 and the quantum chaotic wavepacketsecondary radar target recognition procedure 702, as shown in FIG. 7.

1. The Quantum Chaotic Wavepacket Secondary Radar Signal GeneratingProcedure 700

The fundamental quantum chaotic wavepacket secondary radar signalgenerating procedure 700 mainly generates and transmits the digitalrecurrent quantum chaotic wavepacket secondary radar signal bysuperposing the quantum chaotic wavepacket signature signal on thecaptured quantum chaotic wavepacket primary radar signal. The blockdiagram of the procedure 700 is shown in FIG. 7A, and the procedure 700executes the three procedures sequentially shown in FIG. 7B.

Executing procedure 710: perform the temporal digital correlationbetween the received radar baseband signal s_(r) ¹ and the transmittedquantum chaotic wavepacket primary radar carrier φ_(j3) to get anonnegative correlation value sequence R_(j3) ¹ by the slidinginner-product.

${R_{j\; 3}^{1}(k)} = {{\sum\limits_{n}{{s_{r}^{1}\left( {n + k} \right)}{\phi_{j\; 3}(n)}}}}^{2}$

Executing procedure 711: perform the capture of the quantum chaoticwavepacket primary radar carrier φ_(j3) by seeking the maximum valueR_(max) ¹ in the span 2K of the above nonnegative correlation valuesequence R_(j3) ¹ larger than a specified detection threshold R_(ref) ¹and its corresponding delay k₀ ¹.

$\quad\left\{ \begin{matrix}{{R_{j\; 3}^{1}\left( k_{0}^{1} \right)} = {\max \left\{ {R_{j\; 3}^{1}(k)} \right\}}} \\{{R_{j\; 3}^{1}\left( k_{0}^{1} \right)} > R_{ref}^{1}}\end{matrix} \right.$

Executing procedure 712: generate and transmit the digital recurrentquantum chaotic wavepacket secondary radar signal by superposing thequantum chaotic wavepacket signature carrier φ_(j4) on the capturedquantum chaotic wavepacket primary radar carrier s_(r) ¹ at the capturetime k₀ ¹.

s _(t) ¹(n)=s _(r) ¹(n+k ₀ ¹)+φ_(j4)(n)

2. The Quantum Chaotic Wavepacket Secondary Radar SignalTransmit-Receiving Procedure 701

The fundamental quantum chaotic wavepacket secondary radar signaltransmit-receiving procedure 701 mainly accomplishes the transmissionand reception of the quantum chaotic wavepacket secondary radar basebandsignal. In the transmitter, the quantum chaotic wavepacket basebandsignal ∠_(j3) and s_(t) ¹ are transmitted either directly or frequencyconverted, correspondingly in the receiver the quantum chaoticwavepacket baseband signal s_(r) ¹ and s_(r) or φ_(j3)+φ_(j4) isreceived either directly or frequency converted, as shown in FIG. 2 andFIG. 2A.

3. The Quantum Chaotic Wavepacket Secondary Radar Target RecognitionProcedure 702

The fundamental quantum chaotic wavepacket secondary radar targetrecognition procedure 702 mainly recognizes the interested target andextract its information such as two-way delay by joint correlationdetection shown in FIG. 7C, and executes the five proceduressequentially shown in FIG. 7D.

Executing procedure 720: perform the temporal digital correlationbetween the received radar baseband signal s_(r) and the transmittedquantum chaotic wavepacket primary radar carrier φ_(j3) to get anonnegative correlation value sequence R_(j3)(k), and similarly performthe temporal digital correlation between the received radar basebandsignal s_(r) and the transmitted quantum chaotic wavepacket secondaryradar carrier φ_(j4) to get nonnegative correlation value sequenceR_(j4)(k) by the sliding inner-product.

${R_{j\; 3}(k)} = {{\sum\limits_{n}{{s_{r}\left( {n + k} \right)}{\phi_{j\; 3}(n)}}}}^{2}$${R_{j\; 4}(k)} = {{\sum\limits_{n}{{s_{r}\left( {n + k} \right)}{\phi_{j\; 4}(n)}}}}^{2}$

Executing procedure 721: find the maximum R_(max) and its correspondingtime delay k₀ in the span 2K of the above nonnegative correlation valuesequence R_(j3) (k).

R _(j3)(k ₀)=R _(max)

Executing procedure 722: generate the primary target detectionreturn-to-zero pulse by compare the above maximum primary nonnegativecorrelation value R_(j3) (k₀) with the primary detection thresholdR_(ref).

Executing procedure 723: estimate the two-way delay for the quantumchaotic wavepacket primary radar target by a normalized and weightedsummation of above primary nonnegative correlation value sequenceR_(j3)(k) by the trigger of the above primary radar target detectionreturn-to-zero pulse.

$k = {k_{0} + {\sum\limits_{k = {- K}}^{K}{k\frac{R_{j\; 3}\left( {k_{0} + k} \right)}{R_{\max}}}}}$

Execution procedure 724: calculate the summation of the span from[k]−δ_(n) to [k]+δ_(n) of the secondary nonnegative correlation valuesequence R_(j4)(k) and to output the two-way delay for the quantumchaotic wavepacket secondary radar target by compare the above summationvalue with the recognition threshold R_(j4) _(ref) .

${\sum\limits_{k = {{\lbrack k\rbrack} - \delta_{n}}}^{{\lbrack k\rbrack} + \delta_{n}}{R_{j\; 4}(k)}} > R_{j\; 4_{ref}}$

To have a better understanding of the invention, two embodiments s aredescribed in detail, but are not a limitation to the invention.According to the technical essence of the invention, any simplemodification to the above embodiments should still be within the scopeof the invention. Each embodiment in this specification focuses on thedifferences from other embodiment, which are referred to each other inthe same or similar parts. For system embodiment, the description isrelatively simple because it corresponds to the method embodiment, sothat it can refer to the relevant description of the method embodiment.

What is claimed is:
 1. A method for generating digital quantum chaoticwavepacket signals, comprising the following steps: constructing an N×NHermitian matrix Ĥ; calculating N eigen-wavefunctions φ_(j) of a quantumHamiltonian system with a Hamiltonian by numerical calculation methods,wherein the Hamiltonian is the N×N Hermitian matrix Ĥ; extracting aplurality of eigen-wavefunctions from N eigen-wavefunctions φ_(j) asquantum chaotic eigen-wavefunctions according to a chaos criterion,wherein the plurality of eigen-wavefunctions have chaos features; andgenerating a plurality of semi-classical digital quantum chaoticwavepacket signals φ_(j)(n) with a length N from the quantum chaoticeigen-wavefunctions according to a mathematical correspondence between aclassical signal and a wavefunction in quantum mechanics, wherein theplurality of semi-classical digital quantum chaotic wavepacket signalsand the quantum chaotic eigen-wavefunctions have one mathematical form.2. The method according to claim 1, wherein, the N×N Hermitian matrix Ĥis used as the Hamiltonian of the quantum Hamiltonian system and has thefollowing mathematical expression:${{\hat{H}\left( {x,y} \right)} = {{- \frac{a}{\sigma}}e^{\frac{{({x - y})}^{2}}{b\; \sigma^{2}}}}};$wherein a, b and σ represent a first predetermined constant parameter, asecond predetermined constant parameter and a third predeterminedconstant parameter, respectively.
 3. The method according to claim 2,wherein, the quantum Hamiltonian system with the Hamiltonian has aquantum state chaotic transition, and the plurality ofeigen-wavefunctions have features corresponding to classical chaoticsignals.
 4. The method according to claim 3, wherein, the Neigen-wavefunctions φ_(j) meet the following mathematical constraint:Ĥφ _(j) =E _(j)φ_(j); wherein E_(j) is an energy level of a quantumcorresponding to the N eigen-wavefunctions φ_(j).
 5. The method foraccording to claim 4, wherein, the numerical calculation methodscomprise at least one selected from the group consisting of a Divide andConquer method, and a Jacobian method.
 6. The method f according toclaim 5, wherein, Hermitian external perturbation H′ is added to the N×NHermitian matrix Ĥ to get different eigen-vectors φ_(j) by the numericalcalculation methods, wherein the different eigen-vectors are expressedas follows:(Ĥ+H′)φ_(j) =E _(j)φ_(j).
 7. The method according to claim 1, wherein, aself-power spectral density method is used as the chaos criterion. 8.The method according to claim 7, wherein, according to the chaoscriterion, the momentum spectral density ψ_(j) is calculated byperforming a Fourier Transform on the N eigen-wavefunctions φ_(j). 9.The method for according to claim 8, wherein, according to the chaoscriterion, a chaotic property of the N eigen-wavefunctions φ_(j) isdetermined by the momentum spectral density ψ_(j).
 10. The methodaccording to claim 9, wherein, the N eigen-wavefunctions φ_(j) withextended momentum spectral density is chaotic, and is a quantum chaoticwavefunction.